Prime 5101
 

The prime 5101 is congruent to 3^6 (mod 1093)




Are there infinitely many primes p congruent to 3^k (mod 1093) with k>0?

[QUOTE=enzocreti;513776]Are there infinitely many primes p congruent to 3^k (mod 1093) with k>0?[/QUOTE]

For any positive integer k there are infinitely many primes congruent to 3^k mod 1093, yes. Note that 3 is relatively prime to 1093 (and that 3^k has order 7 mod 1093).

5101
 

[QUOTE=CRGreathouse;513780]For any positive integer k there are infinitely many primes congruent to 3^k mod 1093, yes. Note that 3 is relatively prime to 1093 (and that 3^k has order 7 mod 1093).[/QUOTE]




51001 divides 2^(5101-1)-1.


Just a curio


But maybe a better curio is that 1021 and 1201 divide 2^(5101-1)-1 where 1021 and 1201 are primes with 0 and 2 changed....1021+1201 is 2222...moreover 1801 and 8101 divide 2^5100-1...also here 8 and 1 changed

Amazing that...
 

(2^5100-1)/1021/1201/1801/8101 is congruent to 9393 mod (101^2)




(2^5100-1) is divisible by at least four primes of the form x^2+45*y^2